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A finite element formulation and analysis for advection-diffusion and incompressible Navier-Stokes equations

Liu, Hon Ho
http://rave.ohiolink.edu/etdc/view?acc_num=case1057156956

Abstract Details

1993, Doctor of Philosophy, Case Western Reserve University, Mechanical Engineering.
A Petrov-Galerkin finite element method is presented for the solution of advection-diffusion and incompressible Navier-Stokes equations. The proposed mixed formulation for the primitive variables of velocity-pressure is based on the weighted residual method of 'Streamline Upwind/Petrov-Galerkin' (SUPG), with a specialization for a two-dimensional higher-order biquadratic-bilinear element. The formulation results in a node-dependent intrinsic time τ. A companion formulation for the penalty method is also developed. In addition, discontinuity capturing operators are devised to be added to the SUPG operator to enhance the control of numerical oscillations at shock fronts. Temporal-discretization is achieved by the fully implicit θ-method and a second-order accurate three-level backward-difference scheme. The nonlinear discretized equations are solved through a sequence of linearization and iteration. The algorithm allows both the full or modified Newton-Raphson procedures. The discretized equations of momentum and mass equilibriums are satisfied at every increment or time-step through predictor/multi-corrector iterations. The fully-coupled set of linearized equations from the mixed formulation is solved directly and simultaneously without resolving to "ti me-splitting". In the latter, the conservations of momentum and mass are generally solved in a staggered fashion through the pressure Poisson equation. The direct procedure is chosen because of the benefits of simpler boundary conditions and more accurate computations. Numerical results are presented on various flow problems to demonstrate the robustness and accuracy of the formulation. Among those are the vortex-shedding behind a circular cylinder (Re = 200), and the transient generation and interaction of secondary and tertiary vortices in a square driven cavity (Re = 10,000)
Robert Mullen (Advisor)
219 p.
finite element formulation; advection-diffusion; incompressible Navier-Stokes; equations

Recommended Citations

Citations

  • Liu, H. H. (1993). A finite element formulation and analysis for advection-diffusion and incompressible Navier-Stokes equations [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1057156956

    APA Style (7th edition)

  • Liu, Hon. A finite element formulation and analysis for advection-diffusion and incompressible Navier-Stokes equations. 1993. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1057156956.

    MLA Style (8th edition)

  • Liu, Hon. "A finite element formulation and analysis for advection-diffusion and incompressible Navier-Stokes equations." Doctoral dissertation, Case Western Reserve University, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=case1057156956

    Chicago Manual of Style (17th edition)

case1057156956
1,115
© 1993, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.